The simulations in this chapter were made with the simulator LTE_System_Level_1.6_r885. The LTE downlink OFDMA scenario will be considered in the following simulations. Figure 21 illustrates the mean, edge and peak throughput.
Three different scheduling algorithms were chosen : Round Robin, Best Channel Quality Indicator and Proportional Fair. Closed loop spatial multiplexing with 2x2 antenna configuration, 20 MHz bandwidth and 20 users in the cell. The simulation time is chosen equal to 50 TTI. Where TTI is equal to 1ms. The pathloss model was chosen according to the 3GPP technical specification TS 36.942. The scenario in the following simulation is done for the urban area model. The propagation model is the following:
` = 40(1 − 4 ∙ 10$o∙ pℎ) ∙ log;=(U) − 18 ∙ log;=(pℎ) + 21 ∙ log;=(-) + 80s (10)
Where Dhb is the height of the base station antenna measured in metres from the average rooftop level, R is the base station UE separation in km, and f is the carrier frequency in MHz.
The carrier frequency was taken equal to the 2000 MHz and Dhb = 15 m above the average rooftop level according to the 3GPP technical specification TS 36.942. Then the equation 10 will be in the following form:
` = 128.1 + 37.6 log;=U (11)
After L propagation factor is found the pathloss can be described by the following formula:
]ℎ,\))4 = ` + `\x (12)
Where LogF is the log-normally distributed shadowing with the standard deviation of 10 dB.
For the first mean throughput it can be seen that the Best CQI has the maximum value and the Round Robin has the smallest one. The drawback of the Best CQI scheduler is a very low fairness among the users. It is happennig because this scheduler give the resources only to the user with the best channel conditions. The users that have all the time a bad channel quality will be not scheduled at all. In contrast, the Proportional Fair scheduler has the best fairness among the users. Despite on the very high peak throughput of Best CQI scheduler it is not serving the users that have a bad channel condition, the edge throughput is equal to 0.
Figure 21. UE Throughput comparison for different scheduling algorithms.
mean throughput edge throughput peak throughput 0
10 20 30 40 50 60
throughput (Mbit/s)
2x2 CLSM: 20 MHz bandwidth, 5 km/h Winner II channel, 20 UEs/cell
round robin scheduler. Fairness=0.71 best CQI scheduler. Fairness=0.08 proportional fair scheduler. Fairness=0.85
Figure 22 illustrates the empirical CDF of throughput of different scheduling algorithms. It can be seen that the probability of throughput to be equal to 0 for max CQI scheduler has the very big chances, the ECDF of it is about 0.64. But from the other side it can achieve the higher throughput than Proportional fair and Round Robin schedulers. The black dots on the graphs correspond to the mean value.
Figure 22. The empirical CDF of the throughput of different scheduling algorithms.
0 1 2 3 4 5 6 7 8 9 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
UE throughput (Mbit/s)
UE throughput ECDF
2x2 CLSM: 20 MHz bandwidth, 5 km/h Winner II channel, 20 UEs/cell
2x2 CLSM: round robin scheduler 2x2 CLSM: best CQI scheduler 2x2 CLSM: proportional fair scheduler
Figure 23 compares the throughput of different antenna configurations. The 4x4 antenna configuration can achieve the highest throughput.
Figure 23. The comparison of throughput with different antenna configurations.
0 1 2 3 4 5 6 7 8 9 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
UE throughput (Mbit/s)
UE throughput ECDF
CLSM: 20 MHz bandwidth, 5 km/h Winner II channel, round robin, 20 UEs/cell
2x2 CLSM:
4x2 CLSM:
4x4 CLSM:
Figure 24 compares the throughput of the different antenna configuration regarding to the SINR. When the SINR is less than 5 dB the increasing the number of antenna will not significantly increase the throughput. The result shows that more receiver and transmitter antennas can improve the performance of the system when the SINR is higher than 5 dB.
Figure 24. UE throughput vs. SINR.
-10 -5 0 5 10 15 20 25 30
0 2 4 6 8 10 12
UE Wideband SINR (dB)
UE throughput (Mbit/s)
Wideband SINR-to-throughput mapping
2x2 CLSM:
4x2 CLSM:
4x4 CLSM:
Figure 25. Shannon capacity vs. SNR.
For the following results the LTE_Link_Level_1.7_r1089 simulator were used. Figures 26, 28, 30, 32 give the result of throughput with different transmissions modes:
Transmit Diversity (TxD); Open Loop Spatial multiplexing (OLSM); Single Antenna (SISO) and different number of retransmissions. The simulation time is 5000 TTI or 5000 subframes and the bandwidth is equal to 1.4 MHz. Number of Channel Quality Indicators (CQI) is 7.
Figure 26 illustrates the situation where the number of retransmissions (re-tx) is three.
The channel type is considered as ITU Pedestrian B channel model PedB type according to the Recommendation ITU-R M.1225. The pathloss model for PedB channel is the following:
2 4 6 8 10 12 14 16 18 20
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5x 108
SNR(dB)
Capacity (bit/s)
Capacity in LTE
SISO
MIMO, NT=NR=2 MIMO, NT=NR=4
` = −10 log;=y6√67%z |6− 10 log;=}67zPy;~−67Q~; |6 − 10 log;=(/U)6 (13)
where R is the mobile to base separation,
= $;y|/|| (14)
= (∆ℎ4)6+ 16 (15)
∆ℎ4 is the difference between average mobile height and average building height and x is the distance between mobile and diffracting edges,
d is the average separation between the buildings.
Table 8 gives the rest of the PedB channel’s characteristics.
Table 8. Channel model B. (Recommendation ITU-R M.1225.) Tap channel conditions. The Hybrid Automatic Repeat request (HARQ) is used in LTE for retransmission. Figure 26 and Figure 30 were compared to each other. The channel type is the same and the number of retransmission is different. It is become obvious that the HARQ procedure will not increase the throughput comparing to the procedure with no
HARQ when SNR is higher than 10dB. That mean when the channel is good enough, the packets will not be lost so often and more retransmission is not required.
Figure 26. Throughput vs. SNR with different transmission schemes, the channel type PedB and 3 re-tx.
The Block Error Rate for the PedB channel type is lower than for flat Rayleigh channel type. The difference between BLER curves with HARQ retransmission and with no HARQ is only 2 dB after SNR is more than 0. The transmission mode TxD 4x2 is enhancing the system performance by decreasing the number of erroneous block, the blocks with errors. The OLSM scheme demonstrates the receiving of more blocks with errors. The SISO model has the worst case scenario for the BLER. This shows how the transmission schemes could improve the system performance.
-10 -5 0 5 10 15 20
0 0.5 1 1.5 2 2.5
throughput, CQI 7, 5000 subframes, PedB, 3 re-tx
throughput [Mbps]
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
Figure 27. BLER for PedB channel and 3 re-tx.
The utilization of the transmit diversity scheme TxD 4x2 is showing a better result than OLSM 4x2 for SNR < 5 dB. Thus, the transmit diversity scheme is more beneficial in a situation with low SNR. In case of a better channel quality the OLSM 4x2 scheme is giving the highest throughput in comparison with other transmission modes. The feedback from the user in the case of an open loop spatial multiplexing includes only the number of the transmitted layers and not primary precoding matrix.
-10 -5 0 5 10 15 20
10-3 10-2 10-1 100
BLER, CQI 7, 5000 subframes, PedB, 3 re-tx
BLER
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
For flat Rayleigh channel the situation is almost the same as for PeB channel. The different transmission modes make an effect for the throughput. When the SNR is low the TxD 4x4 illustrates higher throughput then OLSM 4x2. This can be useful to adapt the transmission mode when the channel quality is getting better or worse. When SNR is high enough the OLSM scheme achieves the highest data rate between the rest of the modes demonstrated in the figure.
Figure 28. Throughput vs. SNR with different transmission schemes, the channel type flat Rayleigh and 3 re-tx.
-10 -5 0 5 10 15 20
0 0.5 1 1.5 2 2.5
throughput, CQI 7, 5000 subframes, flat rayleigh, 3 re-tx
throughput [Mbps]
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
Different channel types also bring some changes to the results of BLER. For flat Rayleigh channel the BLER is higher than for the same transmission modes with 3 retransmissions in PedB channel type.
Figure 29. BLER for flat Rayleigh channel and 3 re-tx.
-10 -5 0 5 10 15 20
10-3 10-2 10-1 100
BLER, CQI 7, 5000 subframes, flat rayleigh, 3 re-tx
BLER
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
As it was mentioned before, the number of retransmission is useful with a low SNR.
Figure 30 show that for zero retransmissions the throughput is zero when SNR is less the 0 dB. When SNR is higher than 10 dB the number of retransmissions is not making any differences to the UE throughput.
Figure 30. Throughput vs. SNR with different transmission schemes, the channel type PedB and 0 re-tx.
-10 -5 0 5 10 15 20
0 0.5 1 1.5 2 2.5
throughput, CQI 7, 5000 subframes, PedB, 0 re-tx
throughput [Mbps]
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
Figure 31. BLER for PedB channel and 0 re-tx.
Figure 32. Throughput vs. SNR with different transmission schemes, the channel type flat Rayleigh and 0 re-tx.
-10 -5 0 5 10 15 20
10-3 10-2 10-1 100
BLER, CQI 7, 5000 subframes, PedB, 0 re-tx
BLER
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
-10 -5 0 5 10 15 20
0 0.5 1 1.5 2 2.5
throughput, CQI 7, 5000 subframes, flat rayleigh, 0 re-tx
throughput [Mbps]
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
Figure 33. BLER for flat Rayleigh channel and 0 re-tx.
The CQI mapping is illustrated in Figure 34 and 35. The reports of channel quality indicators (CQI) are used to select the appropriate Modulation and Coding scheme (MCS) for downlink transmissions. For the case with a higher SNR, the CQI value will be also higher. According to Table 9 the different CQI have the different modulation schemes.
Table 9. CQI values. (3GPP TS 36.213 version 9.3.0 Release 9, 2010).
CQI index
Modulation Approximate code
rate
Efficiency (information bits
per symbol)
1 QPSK 0.076 0.1523
2 QPSK 0.12 0.2344
-10 -5 0 5 10 15 20
10-3 10-2 10-1 100
BLER, CQI 7, 5000 subframes, flat rayleigh, 0 re-tx
BLER
SNR [dB]
SISO TxD 2x1 TxD 4x2 OLSM 4x2
3 QPSK 0.19 0.3770
4 QPSK 0.3 0.6016
5 QPSK 0.44 0.8770
6 QPSK 0.59 1.1758
7 16 QAM 0.37 1.4766
8 16 QAM 0.48 1.9141
9 16 QAM 0.6 2.4063
10 64 QAM 0.45 2.7305
11 64 QAM 0.55 3.3223
12 64 QAM 0.65 3.9023
13 64 QAM 0.75 4.5234
14 64 QAM 0.85 5.1152
15 64 QAM 0.93 5.5547
For every different SNR the CQI value is different and the BLER and the throughput are also changing. The flexibility of modulation type makes the LTE system more efficient. In case of a bad channel quality the CQI value will be equal to one and the modulation type will be QPSK, so the distance between symbols will be more and the probability of error and lost packets decreases. The UE uses the PUSCH channel to report the CQI values.
Figure 34 illustrates the BLER for different SNR values. The CQI reports the indicator for every SNR value. When SNR is high, more efficient modulation type is used. It will not increase the erroneous number of packets comparing to the low SNR situation. For the low SNR the CQI value is also lower and the modulation type of transmission is adapting to the current channel quality, the order of modulation becomes lower and the distance between symbols is higher. Thus, it reduces the probability of error to occur.
Figure 34. BLER for 15 MCS.
For a higher CQI value the higher modulation type is used for transmission. When the channel is good the higher order modulation will give a better throughput and the probability of error will be small enough and will not decreases the system performance.
Figure 35. Throughput for 15 MCS.
-20 -10 0 10 20 30